Lesson Objectives
  • Demonstrate an understanding of long division
  • Demonstrate an understanding of division with decimals
  • Learn how to convert a fraction into a decimal

How to Convert a Fraction into a Decimal


In our last lesson, we learned how to divide decimals. This knowledge will enable us to convert a fraction into a decimal. In order to convert a fraction into a decimal:
  • divide the numerator by the denominator
  • Continue the division until the remainder is zero or a repeating digit/series of digits
Let's look at a few examples.
Example 1: Convert each fraction into a decimal
$$\frac{3}{4}$$ We will set up our long division with 3 (dividend) under the long division symbol and 4 (divisor) to the left of the long division symbol: Fraction to Decimal Conversion We can see that 4 is larger than 3. This means we will need to place a decimal point after 3 and add a zero to the right in order to divide. Recall that:
3 = 3.0
Remember to bring the decimal point up into the answer: Fraction to Decimal Conversion Now we can perform our division. We continue to add zeros until we have zero as a remainder or a repeating digit/series of digits: Fraction to Decimal Conversion $$\frac{3}{4} = 0.75$$ Example 2: Convert each fraction into a decimal
$$\frac{9}{20}$$ We will set up our long division with 9 (dividend) under the long division symbol and 20 (divisor) to the left of the long division symbol: Fraction to Decimal Conversion We can see that 20 is larger than 9. This means we will need to place a decimal point after 9 and add a zero to the right in order to divide. Recall that:
9 = 9.0
Remember to bring the decimal point up into the answer: Fraction to Decimal Conversion Now we can perform our division. We continue to add zeros until we have zero as a remainder or a repeating digit/series of digits: Fraction to Decimal Conversion $$\frac{9}{20} = 0.45$$ Example 3: Convert each fraction into a decimal
$$\frac{17}{30}$$ We will set up our long division with 17 (dividend) under the long division symbol and 30 (divisor) to the left of the long division symbol: Fraction to Decimal Conversion We can see that 30 is larger than 17. This means we will need to place a decimal point after 17 and add a zero to the right in order to divide. Recall that:
17 = 17.0
Remember to bring the decimal point up into the answer: Fraction to Decimal Conversion Now we can perform our division. We continue to add zeros until we have zero as a remainder or a repeating digit/series of digits: Fraction to Decimal Conversion $$\frac{17}{30} = 0.5\overline{6}$$